Optimal generation dispatch with wind and solar curtailment

Shulzhenko S.V., PhD (Engin.), Senior Research Scientist, https://orcid.org/0000-0002-7720-0110
Institute of General Energy of the National Academy of Sciences of Ukraine, 172 Antonovycha str., Kyiv, 03150, Ukraine
Language: Ukrainian, English
Source: The Problems of General Energy, 2020, 4(63):14―32
Section: Mathematical modeling of energy facilities and systems
UDC: 621.3:519.8
Received: 17.11.2020
Published: 28.12.2020


To solve the actual task of finding optimal generation mix and dispatch of thermal and nuclear power units, and hydro units of hydro pumped storages of Ukraine to cover day load power profile according to one of possible wind and solar generation curtailment mode the modification of mathematical MIP model is proposed. There are three modes of wind and solar generation curtailment revised in the article: 1) absolute maximum generation curtailment, 2) single for whole day decreased load factor, and 3) one per one hour decreased load factor. The possibility to allocate an exogenously determined level of frequency containment reserves (secondary reserves) on thermal power units is realized in the MIP model.
The calculation’s results analysis shows that among revised wind and solar generation curtailment methods the method 2) is most appropriate in the short term because only administrative measures implementation is required, which could be put into force with appropriate legislation and does not require essential investments or implementation of complicated technical measures. The additional possible positive effect caused by the implementation of method 2) is it makes background for participation wind and solar generation in the ancillary services market and intraday balancing. In the middle term, the gradual implementation of method 3) is the most appropriate decision because a more stable power system balancing mode (minimum import/export amounts) could be provided. Moreover, extra nuclear power units and fewer coal thermal power units could be dispatched that is decreases hazard pollutions and carbon emission.
The MIP model is written using MathProg language, a freeware version of AMPL. As a solver, the GNU GLPK program is used. The overall time for one calculation with standard table PC is about 30 seconds. MIP model could be used both for short-term power system optimal dispatch and for long-term national generation mix development studies under the growth rates of renewable installed capacities.

Keywords: power system, daily load profile, robust decisions, mixed linear-integer problem, frequency containment reserve


  1. Pro Tsili staloho rozvytku Ukrainy na period do 2030 roku: Ukaz Prezydenta Ukrainy vid 30.09.20 No. 722/2019. URL: https://zakon.rada.gov.ua/laws/show/722/2019 (Last accessed: 06.11.2020) [in Ukrainian].
  2. Tsili staloho rozvytku: Ukraina: natsionalna dopovid 2017. URL: http://un.org.ua/images/SDGs_NationalReportUA_Web_1.pdf (Last accessed: 06.11.2020) [in Ukrainian].
  3. Pro rynok elektrychnoi enerhii: Zakon Ukrainy vid 13.04.2017 №2019-VIII. Vidomosti Verkhovnoi Rady (VVR), 2017, № 27-28, st.312.
  4. Roziasnennia schodo obmezhennia heneratsii VES ta SES 7 sichnia 2020 roku. Kyiv: NEK “Ukrenerho”, 2020. URL: https://ua.energy/zagalni-novyny/roz-yasnennya-shhodo-obmezhennya-generatsiyi-ves-ta-ses-7-sichnya-2020-roku/ (Last accessed: 10.11.2020) [in Ukrainian].
  5. Robota enerhosystemy 7–13 veresnia 2020 roku. Kyiv: NEK “Ukrenerho”, 2020. URL: https://ua.energy/zagalni-novyny/robota-energosystemy-7-13-veresnya-2020-roku/ (Last accessed: 10.11.2020) [in Ukrainian].
  6. Pro vnesennia zmin do deiakykh zakoniv Ukrainy schodo udoskonalennia umov pidtrymky vyrobnytstva elektrychnoi enerhii z al'ternatyvnykh dzherel enerhii: Zakon Ukrainy vid 21.07.2020 r. № 810-IX. URL: https://zakon.rada.gov.ua/laws/show/810-20#n95 (Last accessed: 10.11.2020) [in Ukrainian].
  7. Shulzhenko, S.V., Turutikov, O.I., & Tarasenko, P.V. (2019). Model of Mathematical programming with integer variables for determining the optimal regime of loading of hydroelectric pumped storage power plants for balancing daily Profile of electric loads of the power system of Ukraine. The Problems of General Energy, 4(59), 13–23 [in Ukrainian]. https://doi.org/10.15407/pge2019.04.013
  8. Shulzhenko, S.V., Turutikov, O.I., & Ivanenko, N.P. (2020). Mixed-integer linear programming mathematical model for founding the optimal dispatch plan of Ukrainian thermal power plants’ units and hydro pumping storages stations’ units for balancing daily load profile of power system of Ukraine. The Problems of General Energy, 1(60), 14–23 [in Ukrainian]. https://doi.org/10.15407/pge2020.01.014
  9. Shulzhenko, S., Turutikov, O., & Bilenko, M. (2020). Mixed integer linear programming dispatch model for power system of Ukraine with large share of baseload nuclear and variable renewables, 2020 IEEE 7th International Conference on Energy Smart Systems (ESS). Kyiv, Ukraine, 2020. P. 363–368. https://doi.org/10.1109/ESS50319.2020.9160222
  10. Frank Meissner, & Clemens Stiewe. (2019). Curtailment of renewable electricity as a flexibility option Policy Paper PP/04/2019. BE Berlin Economics GmbH. 2019. URL: https://www.lowcarbonukraine.com/wp-content/uploads/LCU_PP04_2019-10_en.pdf (Last accessed: 09.11.2020).
  11. Kies, A., Schyska, B.U., & Von Bremen, L. (2016). Curtailment in a Highly Renewable Power System and Its Effect on Capacity Factors. Energies, 9, 510. URL: https://www.mdpi.com/1996-1073/9/7/510/htm (Last accessed: 09.11.2020). https://doi.org/10.3390/en9070510
  12. Nan Li, Bo Yuan & Fuqiang Zhang. (2018). Study on reasonable curtailment rate of large scale renewable energy. IOP Conf. Ser.: Earth Environ. Sci. 121 052092. URL: https://iopscience.iop.org/article/10.1088/1755-1315/121/5/052092/pdf (Last accessed: 09.11.2020). https://doi.org/10.1088/1755-1315/121/5/052092
  13. Xiaohe Yan, Chenghong Gu, Furong Li & Zhaoyu Wang. (2018). LMP-based Pricing for Energy Storage in Local Market to Facilitate PV Penetration. IEEE Transactions on Power Systems, Vol. 33, No. 3. URL: https://www.researchgate.net/publication/321930875_LMP-based_Pricing_for_Energy_Storage_in_Local_Market_to_Facilitate_PV_Penetration (Last accessed: 09.11.2020). https://doi.org/10.1109/TPWRS.2017.2785286
  14. Zvit z otsinky vidpovidnosti (dostatnosti) heneruiuchykh potuzhnostej (Proekt). Kyiv: NEK “Ukrenerho”, 2020. URL: https://ua.energy/wp-content/uploads/2020/12/Proyekt-zvitu-z-otsinky-vidpovidnosti-dostatnosti-generuyuchyh-potuzhnostej-2020.pdf (Last accessed: 11.11.2020) [in Ukrainian].
  15. Makhorin Andrew. (2016). Modeling Language GNU MathProg / Language Reference – for GLPK. – Version 4.58. February 2016. URL: http://ftp.gnu.org/gnu/glpk/glpk-4.65.tar.gz (Last accessed: 09.11.2020).
  16. GLPK (GNU Linear Programming Kit). URL: https://www.gnu.org/software/glpk/ (Last accessed: 09.11.2020).


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